Do you have a source for the NHL Network part? I haven't seen anything and ESPN isn't televising all the preseason games.
If you look at the schedule on ESPN.com under national tv you see espn+ isn’t listed for games on NHL network (which are listed NHL). Note for the first night which is on espn and is being simulcast on plus, it list both.
NHL Schedule | ESPN
The Athletic also reports NHL Network games will not be included on ESPN+
A viewing guide on how to watch NHL hockey on American television or streaming platforms
Finally ESPN+ has not included any of NHL Network’s games during the regular season, but has picked up the games that have been televised (not every preseason game is televised locally).
It makes sense. Both ESPN+ and NHL Network are considered networks and NHL Network has rights to certain games. Why would cable systems carry NHL Network if their slate of games was also carried on an outlet that is a must subscribe because they have a slate of local games. It is very different than a expensive subscription service like NHL.tv or Center Ice previously. The drop in cost means NHLN games need to be protected.